Quest Triggers

Get weird egg - Enter Hyrule Castle (outdoors area) and reload the area
Remove Mido from Deku entrance - Met Zelda and received Letter
Saria in SFM - Zelda's letter (you don't need ZL but you don't keep the letter if you don't watch ZL cutscene)
Happy Mask Shop open - Showed Zelda's Letter to the guard in Kakariko
Epona's Song available - Wake up Talon as child and talk to him (same for Milk Bottle)
Lon Lon Ranch Cucco collecting game - Woke Talon as child and talked to him
Running Man in field - 3 Spiritual Stones in inventory
Zelda Escape Cutscene (for Ocarina of Time) - 3 Spiritual Stones in inventory
Open the door of time - Enter Temple of Time from outside the temple and Play Song of Time
Nocturne Cutscene - Beat Forest, Fire, and Water Temples, and enter Kakariko from Hyrule Field
Prelude Cutscene - Beat Forest Temple
Able to drop master sword - Beat forest and Prelude Cutscene
Light Arrow Cutscene - Shadow and Spirit Medallions
Rainbow bridge - Shadow Medallion, Spirit Medallion, and Light Arrow in inventory
Lake Hylia Water Rises - Beat Water Temple and watch the cutscene

Owl Triggers

Owl in Lost Woods near Goron City warp - Zelda's Lullaby in inventory
Owl in Lost Woods near SFM - Saria's Song in inventory
Owl in front of Kakariko gone - Zelda's Lullaby in inventory
Owl in Zora's river appears - Met Zelda and received Letter
Owl in Zora's river disappears - Played Zelda's Lullaby to the Sleepless Waterfall in Zora's River
Owl in Hyrule Field near Gerudo Valley disappears - 3 Spiritual Stones in inventory
Owl in Hyrule Field near Lake Hylia disappears - 3 Spiritual Stones in inventory
Owl in DMT will give you a ride down Death Mountain - Have Magic meter